Question

a chemical reaction takes place inside a flask submerged in a water bath. the water bath contains 7.90 kg of water at 36.9°c. during the reaction 141. kj of heat flows out of the bath and into the flask.
calculate the new temperature of the water bath. you can assume the specific heat capacity of water under these conditions is 4.18 j·g⁻¹·k⁻¹. round your answer to 3 significant digits.

Explanation:

Step1: Convert mass to grams

$m = 7.90\ \text{kg} = 7900\ \text{g}$

Step2: Convert heat to joules

$Q = -141\ \text{kJ} = -141000\ \text{J}$ (negative as heat flows out)

Step3: Rearrange heat formula for ΔT

$\Delta T = \frac{Q}{m \cdot c}$

Step4: Calculate ΔT

$\Delta T = \frac{-141000}{7900 \cdot 4.18} \approx -4.27\ \text{K}$ (ΔT in K = ΔT in °C)

Step5: Find new temperature

$T_{\text{new}} = 36.9 - 4.27 = 32.63\ \text{°C}$

Step6: Round to 3 significant digits

$T_{\text{new}} \approx 32.6\ \text{°C}$

Answer:

32.6°C